A New Approach for Generating the TX Hierarchy as well as Its Integrable Couplings

Abstract EN

Tu Guizhang and Xu Baozhi once introduced an isospectral problem by a loop algebra with degree being λ , for which an integrable hierarchy of evolution equations (called the TX hierarchy) was derived under the frame of zero curvature equations.

In the paper, we present a loop algebra whose degrees are 2 λ and 2 λ + 1 to simply represent the above isospectral matrix and easily derive the TX hierarchy.

Specially, through enlarging the loop algebra with 3 dimensions to 6 dimensions, we generate a new integrable coupling of the TX hierarchy and its corresponding Hamiltonian structure.